You familiar with a cassette tape? It's the same principle.
An eight-track is a cartridge with a tape on a continuous loop that has music. The tape was moved by a spinning post up against a rubber wheel (called a pinch roller and capstan) past the tape head. Once you got to the end of the loop, there was a signal that prompted the player to move the head down to the next set of tracks. It's called an eight-track because the left and right side for stereo are a track each, and there are four sets of the two. You could also switch between each of the four sets of tracks by pushing a button.
The upside of the eight-track is that it the tape moved past the head at twice the speed of a cassette tape, making for better treble response, and the tapes were easier to store and care for than vinyl records and also more portable. The downsides were that the players tended to eat the tapes, there was no fast-forward or rewind and because the loop was a single set length, sometimes a song would have to fade out in the middle of it, then the player would switch over, then the song would fade back in and continue.